How can I use hooks for cloth simulation?
Ok I think Nathan has solved the problem. Here are 2 other methods:
First an alternative with empties:

Select each corner vertex and hook it to an empty (CtrlH &gt; Hook To New Object).
Select the 4 corner vertices and create a group that will be the pin group of the cloth simulation:



Don' forget to put the Cloth modifier on the bottom of the modifiers stack, under the 4 Hook. Keyframe the empties, play the animation, bake if necessary:


Or you can use bones:

Create an armature made of 4 bones, parent the cloth object With Empty Groups, select the armature, shift select the cloth object, switch to Weight Paint mode, paint a small surface on each corner for each bone:



Create a new vertex group for the cloth pin, assign it the 4 corners:



Keyframe the bones in Pose mode, play the animation, bake it if necessary:


file: